Least squared vs max inscribed/min circumscribed

Hoping you metrology gurus can shed some light on this. I am a machinist and understand the methodology of min/max but wondering how most inspectors decide when to use this. I’ve done “some” research and honestly it’s all over the board when to use least squared and min/max. Knowing that when you have a tighter tolerance, say +/.0005, the OE is wanting a precision fit whether it be an o ring shaft etc. Functionally I understand on a bore, that a shaft or o ring seal must fit in a bore within the low of the tolerance of that bore roundness taking into account. That being said, when making a part, we do not have a cmm to verify on the floor as we make the parts and use bore gages to monitor through the run. Where the problem rises is we check at the machine in basically a restrained condition(on lathe in chuck) and get the bore to be on size. When it is released we get an out of round condition of roughly .0005. Now when inspection gets it, it will be rejected with max inscribed method and pass with least squared (average) if made to nominal. Is there a general rule when you make components where you don’t know the application and choose between these two methods. We are trying to get a standard on this as we all need to be on the same page. It really doesn’t matter to me or the other machinists which way we choose, but am hoping you guys can help with this. Side note, we don’t always know how the customer will check.

Since you say least squared I'd guess to CMM point fits vs functional gauges.
First thing to remember on a CMM is that no point taken is "right" or correct. Hence fits and lots of points to toss or average out the bad data.
Max inscribed has the same problem of questionable numbers since who knows which are fliers.
Knowing the R&R of the CMM is the base staring point. How many points taken can also move things around.
Least squares will almost always give a different number than functional fit. It cares nothing about runout and is simply the best fit circle to the data points.
It assumes the part to be perfectly round and no error in the collection of points. Both of which are never real world.
One has to know and accept the measuring errors and they have to be very small to the part tolerance. Hence the base rule of ten or hopefully better.
One can write algorithms to toss out what seem to be fliers from lord knows what on max/min inscribed and least square fits but this is not common.
Some decision here is on the part and what it has to do.
Customer and use happy, maker happy.
Bob

I usually use Least Square, unless specified otherwise. Also, Chebyshev used to be an option. I do use CMMs and form testers. So, it mathematically figures each. Basically, Inscribes or circumscribed is used if a shaft rotates in a part. The shaft will ride on three points in a bore. Yes, the whole surface would have to be measured then filtered to 'accurately' get the result. Also, I use a 3 sigma filter to eliminate any dust or fliers.
On some parts, I get to measure at a specific distance. Basically, that is where the mating part will contact. I've had some parts where one point in the measurement would through the part out of tolerance. On one of them, we had to develop where to measure on the surface. This was determined as to where the gasket sealed on the part.
Also, when looking at results, not the Form Fault, also known as Form Error and Form Deviation. Should be a lot less than your tolerance. I had one part come in last year. It was two cones inside the part. So, I could not see them very well. The line gage was showing run out. I was getting a high form fault on the larger of the two cones. The evaluation was in as far as position. I struggled trying to get the FF down. On the CMMs, I want 3 to 5 um for form fault. Yes, on many of the parts I inspect that's my tolerance +/-. The quality tech had the part sectioned. The large cone's surface looked like the metal had been ripped apart. The FF was way worse than reported. You do get some mechanical filtering from whatever probe you use.

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